# Resummation of QED radiative corrections in a strong constant crossed field

## Abstract

By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $$g=\alpha\chi^{2/3}$$, where the dynamical quantum parameter $$\chi=e\sqrt{-(Fp)^2}/m^3$$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $$g\gg1$$. Whereas the breakdown of perturbation theory occurs already for $$g\gtrsim1$$, the leading-order result remains dominant until the asymptotic regime $$g\gg 1$$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Photon Ultrafast Laser Science and Engineering Inst. (PULSE)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); MEPhI Academic Excellence Project; Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”; Russian Foundation for Basic Research (RFBR); German Research Foundation (DFG)

- OSTI Identifier:
- 1660329

- Alternate Identifier(s):
- OSTI ID: 1660472

- Grant/Contract Number:
- AC02-76SF00515; 02.a03.21.0005; 17-12-276-1; 19-02-00643; 19-32-60084; No. 20-52-12046; 361969338

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Mironov, A. A., Meuren, S., and Fedotov, A. M. Resummation of QED radiative corrections in a strong constant crossed field. United States: N. p., 2020.
Web. https://doi.org/10.1103/PhysRevD.102.053005.
```

```
Mironov, A. A., Meuren, S., & Fedotov, A. M. Resummation of QED radiative corrections in a strong constant crossed field. United States. https://doi.org/10.1103/PhysRevD.102.053005
```

```
Mironov, A. A., Meuren, S., and Fedotov, A. M. Mon .
"Resummation of QED radiative corrections in a strong constant crossed field". United States. https://doi.org/10.1103/PhysRevD.102.053005.
```

```
@article{osti_1660329,
```

title = {Resummation of QED radiative corrections in a strong constant crossed field},

author = {Mironov, A. A. and Meuren, S. and Fedotov, A. M.},

abstractNote = {By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $g=\alpha\chi^{2/3}$, where the dynamical quantum parameter $\chi=e\sqrt{-(Fp)^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $g\gg1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.},

doi = {10.1103/PhysRevD.102.053005},

journal = {Physical Review D},

number = 5,

volume = 102,

place = {United States},

year = {2020},

month = {9}

}

https://doi.org/10.1103/PhysRevD.102.053005

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